Question 158
Let $P(n)$ and $Q(n)$ be two polynomials (not constant) with positive integer or zero coefficients. For $n \ge 1$ we determine the sequence $x_n = 2016^{P(n)} + Q(n)$. Prove that there are infinitely many prime numbers $p$ for which there is a positive integer $m$ not divisible by the square of any prime, and for which the condition $p \mid x_m$ holds.
(Oleksiy Klurman)
(Oleksiy Klurman)